1. Field of the Invention
The present invention relates to underwater acoustic measurement systems and, more particularly, to acoustic Doppler current profilers used to measure wave directional spectra and surface wave height.
2. Description of the Related Technology
The use of Doppler sonar to measure currents in a fluid medium is well established. Conventional acoustic Doppler current profilers (ADCPs) typically use an array of acoustic transducers arranged in the well known Janus configuration. This configuration consists of four acoustic beams, paired in orthogonal planes. The ADCP measures the component of velocity projected along the beam axis, averaged over a range cell whose beam length is roughly half that of the emitted acoustic pulse. Since the mean current is assumed to be horizontally uniform over the beams, its components can be recovered simply by differencing opposing beams. This procedure is relatively insensitive to contamination by vertical currents and/or unknown instrument tilts.
The analysis of waves in a fluid medium is much more complicated, however. Although the wave field is statistically stationary and homogeneous, at any instant of time the wave velocity varies across the array and as a result it is not possible to separate the measured along-beam velocity into horizontal and vertical components on a sample-by-sample basis. If one sonar beam is vertical, then the frequency spectra in the can be separated, and a crude estimate of direction obtained from the ratio of horizontal velocity spectra. But phase information is irrevocably lost through this procedure and the estimate is substantially biased when the waves are directionally spread. As a result, this estimator is not particularly useful, except perhaps in the case of swell. There is, however, phase information in the cross-correlations between the various range bins, and this fact allows the application of conventional signal processing techniques to estimate wave direction.
The wave directional spectrum (WDS) is a mathematical representation of the wave direction as a function of azimuth angle and wave frequency, which is useful in describing the physical behavior of waves within the fluid medium. The most common existing devices used to obtain wave directional spectra are 1) pitch, and roll buoys, and 2) PUV triplets, described in further detail below.
Pitch and roll buoys typically measure tilt in two directions as a surrogate for wave slope, along with the vertical component of acceleration. A recent variation uses GPS (Global Positioning System) measurements of three velocity components instead. The measured time series are Fourier transformed and the auto- and cross-spectra are formed, resulting in a cross-spectral matrix at each frequency. The elements of the cross-spectral matrix are directly related to the first five Fourier coefficients in direction (through 2xcex8) of the wave directional spectrum at each frequency (see Appendix A1). These buoys are typically used in deeper water. Unfortunately, the transfer functions for these buoys are complex, non-linear, and often difficult to determine. Additionally, the presence of a mooring line for the buoys adds additional complexity to the analysis due to added motion. Furthermore, such buoys are comparatively costly, vulnerable to weather and theft, and are not capable of measuring currents or wave heights.
PUV triplets (so named due to their measurement of pressure and both components of horizontal velocity, namely u and v) are basically single point electromagnetic current meters having an integral pressure transducer. Time series of pressure and horizontal velocity from PUV triplets are processed in a manner similar to the measurements made by pitch and roll and GPS buoys, also giving only the first five Fourier coefficients in direction at each frequency. PUV triplets are typically bottom mounted, and generally only useful in shallow water. This significant disability is due to the decrease in high frequency response resulting from the decay of wave velocity and pressure with increased water depth.
FIG. 1 illustrates a third and less common prior art technique for measuring wave directional spectrum employed by Krogstad, et al (see xe2x80x9cHigh Resolution Directional Wave Spectra from Horizontally Mounted Acoustic Doppler Current Meters, xe2x80x9d Journal of Atmospheric and Oceanic Technology, Vol. 5, No. 4, August 1988) as part of the CUMEX (Current Measurement Experiment) program. This technique utilizes an acoustic Doppler sonar system having a transducer array mounted on an underwater structure. The array is configured with sets of horizontally oriented acoustic transducers which project two acoustic beams in a horizontal plane 90 degrees apart. Beam propagation is therefore essentially parallel to the surface of the water, and skims the surface of the water as the beam disperses. Such a surface skimming geometry provides a relatively dense and uniform set of time lagged echoes and therefore permits estimation of the joint frequency-wavenumber spectrum S(f,k). See xe2x80x9cOpen Ocean Surface Wave Measurement Using Doppler Sonar, xe2x80x9d Pinkel, R. and J. A. Smith, J. Geophys., Res. 92, 1987. Specifically, the directional spectrum D(xcex8) is expanded into a Fourier series, the coefficients of which are determined from the cross-spectral coefficient matrices generated from data obtained by the system. Since the acoustic beams are horizontal, no vector quantity (i.e., sensitivity vector) relating the beam geometry to the received current data is necessary. This technique is well suited to applications requiring only wave direction measurements and where a large, stable platform, such as a tower or large spar buoy, is available. However, there are a large number of applications, particularly in coastal oceanography and engineering, where it is desirable to know both the wave direction and vertical current profile, which the horizontal beam system can not provide. These applications include the analysis of sediment transport, atmosphere/sea interaction, pollutant dispersal, and hydrodynamic forces on off-shore structures. Additionally, it may be desirable in certain situations to simultaneously obtain wave height data along with the direction and current data. Due to the beam geometry, horizontal beam systems also are unable to measure current velocity above the wave troughs, which may be useful for studies of wave kinematics.
In summary, existing wave direction measurement techniques generally have several significant drawbacks (depending on type) including 1) inability to measure fluid current velocity and/or wave height along with WDS, 2) inability to readily measure wave directional spectrum at a broad range of depths; 3) inability to measure velocity profile above the wave troughs, 4) high degree of non-linearity; 5) high cost relative to the data obtained therefrom; and 6) susceptibility to damage/degradation from surface or near-surface influences.
Accordingly, a system and method for accurately measuring the wave directional spectrum and current profile in a broad range of water depths is needed by both commercial entities and researchers. Such a system and method would further allow the optional measurement of wave height in conjunction with WDS. Additionally, the system would be highly linear in response, physically compact and largely self-contained in design, and could be deployed in a number of different scenarios such as being bottom mounted, moored, or even mounted on a mobile submerged platform. The flexibility of configurations permits the user to have the maximum degree of operational flexibility and device longevity without significantly impacting performance or accuracy. Additional benefits of economy would be obtained through the use of commercially available off-the-shelf broadband or narrowband sonar equipment where practical.
The above-mentioned needs are satisfied by the present invention which includes a system and method for measuring the wave directional spectrum, current velocity within a given range cell or set of range cells, and wave height associated with a fluid medium by using acoustic signals. The present invention allows for accurate measurements of these parameters from fixed, moored, or mobile platforms using conventional Doppler sonar in conjunction with an upward and/or downward looking transducer array.
In a first aspect of the invention, there is an improved system for measuring the wave directional spectrum of a fluid medium. In one embodiment, a broadband acoustic Doppler current profiler (ADCP) is used in conjunction with an upward looking, bottom mounted multi-transducer (or phased) acoustic array to generate multiple acoustic beams, and sample a plurality of different range cells corresponding to different depths within those beams, in order to derive velocity and wave height data. Pressure readings are also optionally obtained from an associated pressure transducer located either on the ADCP or remotely thereto. This velocity, wave height, and pressure data is Fourier-transformed by one or more signal processors within the system (or in post-processing), and a surface height spectrum produced. A cross-spectral coefficient matrix at each observed frequency is also generated from this data. A sensitivity vector specifically related to the ADCP""s specific array geometry is used in conjunction with maximum likelihood method (MLM), iterative maximum likelihood method (IMLM), iterative eigenvector (IEV), or other similar methods to solve the forward relation equation at each frequency and produce a wave directional spectrum. The ADCP may further be used to measure current velocity for various range cells in conjunction with the WDS and wave height measurements.
In a second embodiment of the wave direction measuring system of the present invention, the sonar system and acoustic array are mounted to a platform, such as a vessel hull, with the array positioned so as to generate a plurality of upward and/or downward-looking acoustic beams such that altitude and bottom velocity, along with mean current profile, can be measured.
In a second aspect of the invention, there is an improved algorithm and method of measuring the wave directional spectrum associated with a fluid medium. Specifically, a plurality of vertically oriented (possibly slanted) acoustic beams are generated using the system previously described. A plurality of different range cells within those beams are sampled to derive current velocity (and optionally, wave height) data. Pressure readings are also optionally obtained from the associated pressure transducer. Initially, the sampled data is processed to remove data outliers and calculate mean values for current velocity, depth, and pressure. Intrinsic wave frequency (f) and wavenumber magnitude (k) are also calculated for each observed frequency component. Next, a non-directional surface height spectrum is calculated by computing the power spectra for the range cells of interest, and the transfer functions for the sensor array. A cross-spectral correlation matrix is then generated by selecting data from certain range cells, which may be the same or different from those selected for computing the power spectra above, applying a fast Fourier transform (FFT), cross multiplying all possible pairs of spectral coefficients for each observed frequency, and then averaging the results over time (from repeated Fourier transforms of sequential time segments) and/or over frequency (within bands of adjacent observed frequencies). After the cross-spectral matrix has been obtained, maximum likelihood, iterative maximum likelihood, and/or iterative eigenvector solution methods are applied to the array sensitivity vector, which is uniquely related to the chosen array geometry, and cross-spectral matrix to obtain a frequency specific wave directional spectra. Ultimately, the frequency-specific spectra are combined to construct a complete wave directional spectrum descriptive of both azimuth and frequency. The inventive algorithm can be run on existing signal processing equipment resident within the ADCP system, or run on an external computer as a post-processing task.
In a third aspect of the invention, there is an improved method of measuring the wave height spectrum of a fluid medium using a submerged sonar system. A broadband ADCP sonar system of the type described above is used in conjunction with an upward- or downward-looking transducer array in order to measure wave height using one or a combination of methods. The first method is to determine the slant range to the surface using the measured backscatter intensity and/or signal correlation to interpolate the location of the surface. The wave height spectrum is determined as the power spectrum of the surface elevation. The second method is to measure beam velocity data from selected range cells within the beams and use the relationship between the velocity spectrum and the wave height spectrum from linear wave theory to determine the latter. Alternatively, in a third method, pressure measurements obtained from the ADCP""s pressure transducer may be used to calculate wave height.
These and other objects and features of the present invention will become more fully apparent from the following description and appended claims taken in conjunction with the accompanying drawings.